Answer:
D
Step-by-step explanation:
Recall that for a function [tex]f[/tex] such that [tex]f:X \to Y[/tex], where [tex]X[/tex] is the Domain and [tex]Y[/tex] is the Codomain, the function has a inverse, if and only if, [tex]\forall y \in Y[/tex] exist an unique [tex]x\in X[/tex] such that [tex]f(x)=y[/tex].
[tex]\therefore f^{-1}(y)=x \iff f(x)=y[/tex]
Therefore, the inverse of [tex]f[/tex] for [tex]f(x)=\dfrac{3-x}{7}[/tex] is
[tex]f^{-1} =3-7x[/tex]
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[tex]f(x)=\dfrac{3-x}{7} \implies y= \dfrac{3-x}{7} \implies x=\dfrac{3-y}{7}[/tex]
[tex]x=\dfrac{3-y}{7} \implies 7x = 3-y \implies 7x -3 = -y \implies -7x +3 = y \implies f(x)=3-7x[/tex]
